Alexis Akira Toda

The Double Power Law in Consumption and Implications for Testing Euler Equations

We provide evidence suggesting that the cross-sectional distributions of US consumption and its growth rate obey the power law in both the upper and lower tails, with exponents approximately equal to four. Consequently, high-order moments are unlikely to exist, and the generalized method of moments estimation of Euler equations that employs cross-sectional moments may be inconsistent. Through bootstrap studies, we find that the power law appears to generate spurious nonrejection of heterogeneous-agent asset pricing models in explaining the equity premium. Dividing households into age groups, we propose an estimation approach that appears less susceptible to fat tail issues.

Incomplete Market Dynamics and Cross-Sectional Distributions

The size distributions of many economic variables seem to obey the double power law, that is, the power law holds in both the upper and the lower tails. I explain this emergence of the double power law—which has important economic, econometric, and social implications—using a tractable dynamic stochastic general equilibrium model with heterogeneous agents subject to aggregate and idiosyncratic investment risks. I establish theoretical properties such as existence, uniqueness, and constrained efficiency of equilibrium, and provide a numerical algorithm that is guaranteed to converge. The model is widely applicable: it allows for arbitrary homothetic CRRA recursive preferences, an arbitrary Markov process governing aggregate shocks, and an arbitrary number of technologies and assets with arbitrary portfolio constraints.

Learning curve for paramedic endotracheal intubation and complications

BackgroundPre-hospital laryngoscopic endotracheal intubation (ETI) is potentially a life-saving procedure but is a technique difficult to acquire. This study aimed to obtain a recommendation for the number of times ETI should be practiced by constructing the learning curve for endotracheal intubation by paramedics, as well as to report the change in the frequency of complications possibly associated with intubation over the training period.MethodsUnder training conditions, 32 paramedics performed a total of 1,045 ETIs in an operating room. Trainees performed ETIs until they succeeded in 30 cases. For each patient, the number of laryngoscopic maneuvers and any complications potentially associated with ETI were recorded. We built a generalized logistic model to construct the learning curve for ETI and the frequency of complications.ResultsDuring the training on the first 30 patients the rate of ETI success at the first attempt improved from 71% to 87%, but there was little improvement during the first 13 cases. The frequency of complications decreased from 53% to 31%. More laryngoscopic maneuvers and longer operation time increased complications.ConclusionsIt seems that 30 live experiences of performing an ETI is sufficient for obtaining a 90% ETI success rate, but there seems to be little benefit with fewer than 13 experiences. The frequency of complications remained at a high level even after the training. It is desirable to conduct a more detailed and rigorous evaluation of the benefit of pre-hospital ETI by controlling for the skill level of paramedics.

Securitization and Leverage in General Equilibrium

Although securitization is widely used in reality, few general equilibrium models have collateralized lending, default, and asset-backed securities as key elements. In this paper I develop a highly tractable, heterogeneous agent, incomplete markets dynamic stochastic general equilibrium model with these features. In the model, agents who face aggregate and idiosyncratic investment risk can borrow by putting up their investments as collateral. Borrowers can default at any time, with the only penalty being the confiscation of collateral. The debt contracts are pooled, issued as asset-backed securities, and held by agents in equilibrium. I define the equilibrium concept and prove the existence. The equilibrium allocation weakly Pareto dominates the autarky allocation, but strictly Pareto dominates only if there is active default. Assets in zero net supply are irrelevant for risk sharing when agents have a common relative risk aversion. Numerical examples show that as the collateral requirement loosens, borrowing rates and individual welfare (given wealth) increase and inequality decreases. With only one investment technology, economic growth is hurt because more risk sharing induces less precautionary saving. With two or more technologies, however, asset-backed securities typically enhance economic growth because agents allocate more of their capital to the risky but high return technology.

THE IMPACT OF MEDIA REPORTS ON THE 2008 OUTBREAK OF HYDROGEN SULFIDE SUICIDES IN JAPAN

Objective: Japan experienced a nationwide outbreak of hydrogen sulfide suicides (HSS) between April and May 2008. The annual number of HSS skyrocketed from 19 in 2007 to 1,056 in 2008. However, the factors affecting this enormous increase remain unknown. The present study aimed to examine the effect of media coverage of the incidents on the subsequent epidemic of HSS. Method: We collected time series data from the 1st week of February to the last week of September 2008 (34 weeks), including the number of HSS (St), the number of articles on HSS published in the five major newspapers (Nt), and the number of Internet searches with the keyword “hydrogen sulfide suicide” (Gt). The generalized method of moments was applied to model the concurrent effects of Nt and Gt on St. Results: The increase in the number of newspaper articles significantly induced the increase in HSS (coefficient, 0.84; 95% confidence interval (CI), 0.28–5.3), while the number of Internet searches did not significantly affect the number of HSS (coefficient, −0.75; 95%CI, −19.3–0.45). Conclusions: Exposure to information on HSS from newspaper articles could have directly affected the subsequent increase in the number of suicides. On the other hand, the number of the Internet searches did not have a direct influence on HSS.

Discretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Moments

Approximating stochastic processes by finite-state Markov chains is useful for reducing computational complexity when solving dynamic economic models. We provide a new method for accurately discretizing general stochastic processes by matching low order moments of the conditional distributions using maximum entropy. In contrast to existing methods, our approach is not limited to linear autoregressive processes. We apply our method to numerically solve asset pricing models, with various shock distributions with or without stochastic volatility, and find that it outperforms the solution accuracy of existing global methods by orders of magnitude. The performance of our method is robust to parameters such as the number of grid points and the persistence of the process.Approximating stochastic processes by finite-state Markov chains is useful for reducing computational complexity when solving dynamic economic models. We provide a new method for accurately discretizing general Markov processes by matching low order moments of the conditional distributions using maximum entropy. In contrast to existing methods, our approach is not limited to linear Gaussian autoregressive processes. We apply our method to numerically solve asset pricing models with various underlying stochastic processes for the fundamentals, including a rare disasters model. Our method outperforms the solution accuracy of existing methods by orders of magnitude, while drastically simplifying the solution algorithm. The performance of our method is robust to parameters such as the number of grid points and the persistence of the process.

A Note On The Size Distribution Of Consumption: More Double Pareto Than Lognormal

The cross-sectional distribution of consumption is commonly approximated by the lognormal distribution. This note shows that consumption is better described by the double Pareto-lognormal distribution (dPlN), which has a lognormal body with two Pareto tails and arises as the stationary distribution in recently proposed dynamic general equilibrium models. dPlN outperforms other parametric distributions and is often not rejected by goodness-of-fit tests. The analytical tractability and parsimony of dPlN may be convenient for various economic applications.

Do You Save More or Less in Response to Bad News? A New Identification of the Elasticity of Intertemporal Substitution

We define the elasticity of intertemporal substitution (EIS) for general recursive preferences and identify sharp comparative statics from a general dynamic portfolio choice problem. In many cases, when preferences are homothetic, if EIS is smaller (larger) than 1, an investor will decrease (increase) current consumption in response to bad news about the future. Examples of bad news include (i) becoming more risk averse, (ii) less investment opportunities, (iii) riskier returns, or (iv) more uncertainty about the distribution of returns. Bad news effectively raises the price of future continuation utility, which produces the same qualitative changes in savings rates as lowering the interest rate. Similar results hold for the consumption response to changes in business investment opportunities in an extension to entrepreneurs making joint consumption, financial investment, and capital accumulation decisions. We also provide guidance on simple empirical tests for this condition on EIS based on our comparative statics results.

Discretizing distributions with exact moments: Error estimate and convergence analysis

© 2015 Society for Industrial and Applied Mathematics. The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating distribution by minimizing the Kullback-Leibler information (relative entropy) of the unknown discrete distribution relative to an initial discretization based on a quadrature formula subject to some moment constraints. We study the theoretical error bound and the convergence of this approximation method as the number of discrete points increases. We prove that (i) the theoretical error bound of the approximate expectation of any bounded continuous function has at most the same order as the quadrature formula we start with, and (ii) the approximate discrete distribution weakly converges to the given continuous distribution. Moreover, we present some numerical examples that show the advantage of the method and apply to numerically solving an optimal portfolio problem.

Securitized Markets, International Capital Flows, and Global Welfare

We study the effect of collateralized lending and securitization on the global supply of securitized assets, welfare, and international net and gross capital flows in a two country general equilibrium model with idiosyncratic investment risk. The financial sectors in the two countries, Home and Foreign, differ by the collateral requirement for investment loans, with Home requiring lower margins. In autarky, Home endogenously supplies more assets and enables more risk sharing. Upon financial integration, capital flows from Foreign to Home, leading to lower interest rates and an increase in the global supply of assets. Foreign enjoys substantial welfare gains through better risk sharing and portfolio reallocation, while the welfare experience for Home is ambiguous. Gross capital flows arise when agents face aggregate shocks to the expected payoff to investment projects, but can collapse when shocks concern the variance of returns.